Paul Byron and Alex Galchenyuk also scored for Montreal in a matchup of Original Six franchises already eliminated from playoff contention. Price made 26 saves for his first win since Feb. 4. He had been 0-5-2 since then.

Gustav Nyquist and Tyler Bertuzzi scored for Detroit, and Jared Coreau stopped 27 shots in his fifth game of the season. He is 0-4-0.

Both the Canadiens and Red Wings will take part in the draft lottery this spring. Montreal is 26th in the overall NHL standings, three points ahead of 27th-place Detroit.

The Red Wings have won just once in their last 14 games (1-12-1).

With the two goals, Gallagher pushed his total to 49 points this season. His previous career high was 47.

Gallagher scored his first of the game and team-leading 29th of the season at 4:27 of the second period to give the Canadiens a 2-1 lead. The forward threw the puck on net from the corner of the ice and it bounced off Red Wings defenseman Danny DeKeyser's skate and in.

The Edmonton native, who has scored in three consecutive games, got his 30th at 9:32 when he tipped a shot by Mike Reilly on net. The puck went off Coreau's skate and landed in the crease before the goalie accidentally knocked it in himself.

Gallagher came within inches of his first career hat trick. With 4:26 remaining, Jeff Petry's shot from the blue line trickled past Coreau. Gallagher came close to knocking it in, but Galchenyuk got his stick on it first to make it 4-2.

Bertuzzi got one back for Detroit at 13:41 of the second when he squeezed a loose puck between Price's pads.

The teams traded goals in the first period.

Nyquist got the first at 4:41 with a hard one-timer before Byron responded, on the power play, with a backhand off the post and in at 18:11 for his 19th.

NOTES: Several Canadian Olympians were honored in a pregame ceremony, including medalists Kim Boutin, Charles Hamelin, Justine Dufour-Lapointe and Mikael Kingsbury. ...Holland native Luke Witkowski was a healthy scratch for Detroit.

UP NEXT

Red Wings: Host the Pittsburgh Penguins on Tuesday night.

Canadiens: Play at Pittsburgh on Saturday night.

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